If (10^k · 100^3)/(1000^2) = 10^5, what is the value of k?

Correct answer: 5

The governing concept is expressing every quantity as a power of the same base, 10. We have 100 = 10^2, so 100^3 = (10^2)^3 = 10^6. Similarly, 1000 = 10^3, so 1000^2 = (10^3)^2 = 10^6. Substituting these values gives (10^k · 10^6)/10^6 = 10^k, because equal powers in the numerator and denominator cancel. The equation therefore reduces to 10^k = 10^5. Since the base 10 is positive and not equal to 1, equal powers have equal exponents, so k = 5. Thus option C is correct. The values 3, 4, and 6 would produce 10^3, 10^4, and 10^6 respectively after simplification, so none of them can equal 10^5.